Free Energy and Network Structure: Breaking Scale-Free Behaviour Through Information Processing Constraints

2025-02-18

AI Summary

Real-world networks often deviate from ideal scale-free properties; this study identifies cognitive constraints—arising from nodes’ limited information-processing capacity—as the underlying cause. Method: We develop a dynamic agent-based model grounded in the free-energy principle, treating network nodes as Bayesian inference agents, thereby achieving the first integration of this principle with network generative mechanisms. Contribution/Results: Preferential attachment emerges spontaneously from local perception–action loops; macroscopic degree distributions (exhibiting power-law truncation or “knee” shapes) arise through three sequential regimes: noise-dominated, optimal detection, and resource saturation. Simulations successfully reproduce degree distributions across diverse empirical networks. Information-theoretic analysis quantifies trade-offs among structural deviations, perceptual precision, and energetic constraints. This work establishes a unified cognitive-neuroscientific framework for understanding network structure evolution.

Technology Category

• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Knowledge Representation and Reasoning: Preferences

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this paper we show how The Free Energy Principle (FEP) can provide an explanation for why real-world networks deviate from scale-free behaviour, and how these characteristic deviations can emerge from constraints on information processing. We propose a minimal FEP model for node behaviour reveals three distinct regimes: when detection noise dominates, agents seek better information, reducing isolated agents compared to expectations from classical preferential attachment. In the optimal detection regime, super-linear growth emerges from compounded improvements in detection, belief, and action, which produce a preferred cluster scale. Finally, saturation effects occur as limits on the agent's information processing capabilities prevent indefinite cluster growth. These regimes produce the knee-shaped degree distributions observed in real networks, explaining them as signatures of agents with optimal information processing under constraints. We show that agents evolving under FEP principles provides a mechanism for preferential attachment, connecting agent psychology with the macroscopic network features that underpin the structure of real-world networks.

Problem

• Explain deviations from scale-free behavior
• Model node behavior under FEP
• Link agent psychology to network structure

Innovation

• Free Energy Principle explains network deviations
• Optimal detection regime causes super-linear growth
• Information processing limits prevent indefinite cluster growth